User:Cayennecode
From Wikipedia, the free encyclopedia
[edit] Why .999... != 1 ( why .99999999999... does not equal 1 )
Algebraic Disproof
| assertion | 10 × 0.999… = 9.999… |
| assertion | c = 0.999… |
| step 1 | 10c = 9.999… |
| step 2 | 10c - c = 9.999… − c |
| step 3 | 9 = 9 |
| proof | c != 1 |
Above is the correct breakdown, and below is how the proponent of .999... = 1 believes he's proved his theory: notice he makes an odd jump of from Step 2 to Step 3.
| assertion | 10 × 0.999… = 9.999… |
| assertion | c = 0.999… |
| step 1 | 10c = 9.999… |
| step 2 | 10c - c = 9.999… − 0.999… |
| step 3 | 9c = 9 |
| proof | c = 1 |
A problem I see is with the algebraic equation in the proponent's Step 3, written as 9c = 9. This is incorrect. It should be 9 = 9.
Step 1 is: (10 * c) - c = 9.999.. - c;
So we process (10 * c), resulting in 9.999... and then removed c from both sides of the equation, leaving 9 = 9, not 9c = 9.
Well, you can do this with any variable, like this:
10x = 40.
10x - x = 40 - x.
36 = 36.
36/36 = 36/36.
x doesn't equal 1, x = 4.
Nor is c equal to 1, c = .999...
If you want further proof that .999... != 1, try getting 1 to equal .999... hah = )
The con was great fun though, thanks = )
